8 ≡ 15 (mod 8) is false; the correct answer is 5 ≡ 10 (mod 5) is true.

The standard equation of a circle with center (0, 0) and radius r is x^2 + y^2 = r^2. Here, r = 5, so r^2 = 25.

Parallel lines have the same slope. The slope of y = -3x + 4 is -3, so any line with the same slope, like y = -3x + 1, is parallel.

Distributing 2 gives 2 * x + 2 * 3 = 2x + 6.

Using the property of exponents that states a^m * a^n = a^(m+n), we combine the exponents: 2x + (x + 1) = 3x + 1.

Since 1000 is 10^3, log_10(1000) = 3.

Using the Binomial Theorem, the coefficient of x^3 is given by C(5,3) * (2^3) * (3^2) = 10 * 8 * 9 = 720.

The vertex of the quadratic equation is given by the point (-b/2a, f(-b/2a)).

The function f(x) = 1/(x - 2) has a vertical asymptote at x = 2, where the function is undefined.

A horizontal line represents a function that is constant, meaning it neither increases nor decreases.

A quadratic function is represented by a parabola, which can open either upwards or downwards.

Exponential functions grow or decay at a constant percentage rate, which is a defining characteristic.

Irrational numbers are characterized by their non-repeating, non-terminating decimal expansion, distinguishing them from rational numbers.

The hexadecimal system is a base-16 system that includes the digits 0-9 and letters A-F.

Partners often enter into partnerships to share risks and responsibilities associated with running a business.

The Binomial Theorem is specifically used for expanding expressions of the form (x + y)^n.

For a number to be divisible by 11, the difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11.

The y-intercept is defined as the point where the line crosses the y-axis, which occurs when x is zero.

To check for divisibility by 7, you can double the last digit and subtract it from the rest of the number.

Unlimited liability for all partners is a significant disadvantage, as partners can be personally responsible for business debts.

The polynomial x^2 - 9 can be factored as (x - 3)(x + 3).

An isosceles triangle is defined as having at least two sides that are equal in length.

The roots of the polynomial can be found by factoring it as (x-2)(x-3) = 0, giving roots 2 and 3.

A number is divisible by 10 if it ends in 0.

All listed methods are valid for solving systems of linear equations.

A regular polygon is defined as a polygon with all sides and angles equal, and it cannot be concave; it must be convex.

A circle is defined as a round shape with no corners.

In a square, all angles are right angles (90 degrees), not acute.

In a geometric progression, the common ratio cannot be zero, as it would invalidate the progression.

The sum of the terms in a harmonic progression is not necessarily an integer, as the terms can be fractions.